Nematics with quenched disorder have been repeatedly predicted to form glass phases. Here we present turbidity experiments and computer simulations aimed at studying glass key features such as dynamics and history dependence in randomly perturbed nematics. Electric field-cooling alignment has been employed to prepare samples in suitably oriented starting states. Remarkable remnant order and slow dynamics are found both by experiment and simulations, indicating that random disorder can, by itself, induce a nematic glass state even without perturber restructuring.